Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
160 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14581735 | C2 | semidirect |
| 2. C2×#14581731 | C2 | semidirect |
| 3. #19127939 | C2 | semidirect |
| 5. #19127526 | C2 | semidirect |
| 6. #19127503 | C2 | semidirect |
| 7. #358×C83 | C2 | semidirect |
| 33. C83⋊C16 | D4 | semidirect |
| 76. C83 | #2220 | semidirect |
| 82. #358 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581735 | 2 |
| C2×#14581731 | 2 |
| #19127939 | 2 |
| #19127938 | 2 |
| #19127526 | 2 |
| #19127503 | 2 |
| #358×C83 | 2 |
| #2220 | 83 |